# How do you know why Rolle's Theorem does not apply to #f(x)= x^(2/3)# on the interval [-1,1]?

##### 1 Answer

Apr 18, 2015

**H1**

Is the function continuous on the closed interval?

Yes, power functions are continuous on their domains.

**H2**

Is the function differentiable on the open interval?

No.

(By the way, **H3**

Also by the way: This function does not satisfy the **conclusion** of Rolle's Theorem on any interval, because there is no solution to: